Question

Select the equation that is the inverse of the given function.

f(x) = x-3/5

A. f^-1(x) = 5x + 15
B. f^-1(x) = 5x + 3
C. f^-1(x) = 3x - 5
D. f^-1(x) = - 5/3x

Answer 1

To find the inverse of the function f(x) = (x-3)/5, we need to solve for y, switch x and y, and find f^{-1}(x) = 5x + 3, which corresponds to option B.

Step-by-step explanation:

Inverting a function means finding a new function that "undoes" the original. To find the inverse of the function f(x) = \frac{x-3}{5}, we need to solve for x in terms of y, and then switch x and y. Here are the steps:

1. Start with y = \frac{x-3}{5}.
2. Multiply both sides by 5 to get 5y = x - 3.
3. Add 3 to both sides to find x by itself: 5y + 3 = x.
4. Now, switch x and y to get y = 5x + 3.

So, the inverse function is f^{-1}(x) = 5x + 3, which corresponds to option B.